# Stokes theory of thin-film rupture

## TL;DR

This paper investigates the flow dynamics leading to thin-film rupture due to van der Waals forces, revealing a universal self-similar solution that differs from lubrication theory predictions.

## Contribution

It demonstrates that near rupture, the flow transitions from lubrication theory to a universal Stokes flow solution, providing new insights into thin-film rupture dynamics.

## Key findings

- Lubrication theory predicts $h_{min} \,\propto\, \tau^{1/5}$.
- Near rupture, flow follows a universal self-similar solution with $h_{min} \,\propto\, \tau^{1/3}$.
- The opening angle near rupture is approximately 37 degrees.

## Abstract

The structure of the flow induced by the van der Waals destabilization of a non-wetting liquid film placed on a solid substrate is unraveled by means of theory and numerical simulations of the Stokes equations. Our analysis reveals that lubrication theory, which yields $h_{\text{min}} \propto \tau^{1/5}$ where $h_{\text{min}}$ is the minimum film thickness and $\tau$ is the time until breakup, cannot be used to describe the local flow close to rupture. Instead, the slender lubrication solution is shown to experience a crossover to a universal self-similar solution of the Stokes equations that yields $h_{\text{min}} \propto \tau^{1/3}$, with an opening angle of $37^{\circ}$ off the solid.